Torus Knots and the Topological Vertex

We propose a class of toric Lagrangian A-branes on the resolved conifold that is suitable to describe torus knots on S ³. The key role is played by the \({SL(2, \mathbb{Z})}\) transformation, which generates a general torus knot from the unknot. Applying the topological vertex to the proposed A-branes, we rederive the colored HOMFLY polynomials for torus knots, in agreement with the Rosso and Jones formula. We show that our A-model construction is mirror symmetric to the B-model analysis of Brini, Eynard and Mariño. Compared to the recent proposal by Aganagic and Vafa for knots on S ³, we demonstrate that the disk amplitude of the A-brane associated with any knot is sufficient to reconstruct the entire B-model spectral curve. Finally, the construction of toric Lagrangian A-branes is generalized to other local toric Calabi–Yau geometries, which paves the road to study knots in other three-manifolds such as lens spaces.     

Channel Coordination with Cooperative Advertising Considering Effect of Advertising on Willingness to Pay

In this paper, cooperative advertising in a manufacturer–retailer supply chain is studied. Advertising can enhance willingness to pay (WTP) of customers. This trade-off between the benefits of increasing WTP of customers and the advertising expenditure is a key to understanding the retailers optimal advertising decision. On the other hand, it is interesting to understand in which condition supporting the retailer for his advertising expenditure is beneficial for the manufacturer. In this study, in order to capture pricing and advertising strategies of the channel member, three non-cooperative games including Nash, Stackelberg retailer and Stackelberg manufacturer game-theoretic models are established. In spite of the related studies which restrict price in order to prevent negative demand, the proposed model allows channel members to increase their prices by enhancing WTP of customers. In this study, contrary to similar additive form demand functions applied in the co-op ad literature which limits their studies for cases that profit function is concave with respect to variables, optimal prices and advertising strategies are obtained for all the solution space. Surprisingly for the very high values of the advertising effect coefficient, a finite optimal advertising expenditure is achieved.     

Least-squares finite element methods for the Navier-Stokes equations for generalized Newtonian fluids

In this contribution we present the least-squares finite element method (LSFEM) for the incompressible Navier-Stokes equations. In detail, we consider a non-Newtonian fluid flow, which is described by a power-law model, see [1]. The second-order problem is reformulated by introducing a first-order div-grad system consisting of the equilibrium condition, the incompressibility condition and the constitutive equation, which are written in residual forms, see [2]. Here, higher-order finite elements which are an important aspect regarding accuracy for the present formulation are investigated. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stochastic optimization of an urban rail timetable under time‐dependent and uncertain demand

Urban rail planning is extremely complex, mainly because it is a decision problem under different uncertainties. In practice, travel demand is generally uncertain, and therefore, the timetabling decisions must be based on accurate estimation. This research addresses the optimization of train timetable at public transit terminals of an urban rail in a stochastic setting. To cope with stochastic fluctuation of arrival rates, a two‐stage stochastic programming model is developed. The objective is to construct a daily train schedule that minimizes the expected waiting time of passengers. Due to the high computational cost of evaluating the expected value objective, the sample average approximation method is applied. The method provided statistical estimations of the optimality gap as well as lower and upper bounds and the associated confidence intervals. Numerical experiments are performed to evaluate the performance of the proposed model and the solution method.     

MWCNTs@NHBut/PTA: New efficient solid acid catalyst for solvent free synthesis of benzochromenopyrimidines

In this study, a novel and eco‐friendly synthesis of benzochromenopyrimidines catalyzed by phosphotugstic acid immobilized on aminated multiwalled carbon nanotubes (MWCNTs@NHBut/PTA) is reported. New solid acid catalyst was prepared through a simple process with good percentage of organo metallic groups and characterized with FTIR, TEM, SEM, EDX and TGA techniques. Reusable catalytic system provides a convenient, safe and green pathway to generate a variety of benzochromenopyrimidines under mild conditions.     

Ag3[PMo12O40]: An efficient and green catalyst for the synthesis of highly functionalized pyran‐annulated heterocycles via multicomponent reaction

A facile, efficient and eco‐friendly catalytic protocol was developed for the synthesis of medicinally important pyran‐annulated heterocycles via multicomponent reaction (MCR). Cyclocondensation of differently substituted aromatic aldehydes, malononitrile/ethyl cyanoacetate and various β‐dicarbonyl compounds in the presence of Ag₃[PMo₁₂O₄₀]?nH₂O as heterogeneous catalyst, in EtOH–H₂O, afforded diverse pyran‐fused chromene analogues. The merits observed for this approach were it being conducted via MCR, using commercially available or easily accessible starting materials in the presence of a green and easily separable heterogeneous and reusable catalyst, and affording high yields of desired products in very short reaction times with high purity in one‐pot fashion, thus providing a superior alternative approach for the synthesis of pyran‐annulated heterocycles.     

Synthesis of mesoporous functional hematite nanofibrous photoanodes by electrospinning

Iron(III) oxide (hematite, Fe₂O₃) nanofibers, as visible light‐induced photoanode for water oxidation reaction of a water splitting process, were fabricated through electrospinning method followed by calcination treatment. The prepared samples were characterized with scanning electron microscopy, and three‐electrode galvanostat/potentiostat for evaluating their photoelectrochemical (PEC) properties. The diameter of the as‐spun fibers is about 300 nm, and calcinated fibers have diameter less than 110 nm with mesoporous structure. Optimized multilayered electrospun α‐Fe₂O₃ nanostructure mats showed photocurrent density of 0.53 mA/cm² under dark and visible illumination conditions at voltage 1.23 V and constant intensity (900 mW/cm²). This photovoltaic performance of nanostructure mats makes it suitable choice for using in the PEC water splitting application as an efficient photoanode. This method, if combined with appropriate flexible conductive substrate, has the potential for producing flexible hematite solar fuel generators. Copyright © 2015 John Wiley & Sons, Ltd.     

Preparation of PbO nanocrystals via decomposition of lead oxalate

The present study reports the preparation and characterization of PbO nanocrystals obtained via a thermal decomposition route. The PbO nanocrystals were synthesized using lead oxalate powder as a precursor. Nanostructured products were investigated by means of XRD, TEM, FT-IR and XPS. The XRD results indicate that tetragonal phase β-PbO with a particle size of about 30–45 nm was obtained when the intermediate precipitate was calcined at 500 °C.     

Multi-component synthesis of highly substituted imidazoles catalyzed by nanorod vanadatesulfuric acid

Nanorod vanadatesulfuric acid (VSA NRs), as a recyclable and eco-benign catalyst, was used for one-pot synthesis of 2,4,5-trisubstituted imidazoles and 1,2,4,5-tetrasubstituted imidazoles using aldehydes, benzil, benzoin or 9,10-phenanthrenequinone and ammonium acetate or aniline under solvent-free conditions providing high to excellent yields. VSA is easily prepared by a simple reaction of chlorosulfonic acid and sodium metavanadate in high purity. As compared with the conventional procedures, the present protocol offers several advantages such as simplicity of procedure, short reaction time, high yields, easy workup, recoverability and reusability of the catalyst and simple purification of the products.     

Adsorptive Stripping Voltammetric Determination of Ultra Trace of Zinc and Lead with Carbidopa as Complexing Agent in Food and Water Samples

In the present work, the cathodic stripping voltammetric methodology using a hanging mercury drop electrode was described for simultaneous determination of lead and zinc in different real samples. The method is based on adsorption of metal ions on mercury electrode using carbidopa as a suitable complexing agent. The potential was scanned to the negative direction and the differential pulse stripping voltammograms were recorded. Optimal conditions were found to be: accumulation time; 70 s, accumulation potential; 50 mV versus Ag/AgCl, scan rate; 40 mV s^?1, supporting electrolyte; 0.01 M ammonia buffer at pH 8.5, and concentration of carbidopa; 8.0 μM. The relationship between the peak current versus concentration was linear over the range of 0.1–210 and 0.2–170 nM for lead and zinc, respectively. The detection limits are 0.09 and 0.15 nM for lead and zinc ions respectively. The relative standard deviations at a concentration level of 70 nM of both metal ions are found 1.08 and 1.24% for lead and zinc ions respectively.